[math-fun] n = 562576374032409

Integer n = 562576374032409 is unique in the sense that n and n+1 are sums of two cubes: n = 60684^3 + 69734^3, n+1 = 65521^3 + 65522^3 and also n is the taxi-cab number: n = 60684^3 + 69734^3 = 65340^3 + 65702^3. Is n the least such number? Are there larger such numbers? Zak